injection at different conditions and scales Odd Andersen and Halvor - - PowerPoint PPT Presentation

Simplified models for thermal effects of CO2 injection at different conditions and scales

Odd Andersen and Halvor Møll Nilsen, SINTEF Digital, Norway TCCS, 14th June 2017

Motivation

◮ Thermal effects from injection will affect:

◮ fluid flow ◮ geomechanics ◮ geochemistry

◮ Fully resolved, fully coupled models are expensive. ◮ Can we model the thermal field using simplified models?

◮ Are vertical equilibrium models adequate when modeling the heat

front

◮ To what extent does the overburden need to be taken into account 2 / 22

Conceptual model

r

• verburden

(convection only)

aquifer

(advection and convection)

underburden

(convection only)

Q CO2 plume front

tip mean pos. inner pos.

thermal front

inner pos. tip mean pos. thermal bleed

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Flow models

Full 3D ◮ CO2 saturation ◮ pressure ◮ temperature → One value per cell

r

3D grid

Vertical Equilibrium 1 ◮ plume thickness ◮ caprock pressure ◮ temperature → One value per vertical pillar Vertical Equilibrium 2 → as above, but two temperature values per vertical pillar (CO2 and brine)

r

VE grid

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Overburden models

High vertical resolution

r 2L′

c Low vertical resolution

r

Adiabatic (ignore bleed)

r L′

c = 2√tendD′ (“bleeding length scale”)

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Heat flow and grid resolution

◮ We compare with the continuous case of 1D heat diffusion:

◮ ∂tT − ∂z(D∂zT) = 0 for z ∈ [0, inf] ◮ T(z, 0) = T0 ∀z ∈ [0, ∞) ◮ T(0, t) = T1 ∀t ∈ (0, tend] ◮ → Solution: T(z, t) = T0 + (T1 − T0)erfc(z/Lc) ◮ Heat leaked by time t then equals 2(T1 − T0)

• Dt

π

◮ Finite-volume solution if domain consists of single gridcell of length

2Lc:

◮ T(t) = T0 + (T1 − T0)

• 1 − e

−

t 8tend

• ◮ Heat leaked by time t then equals 2Lc(T1 − T0)
• 1 − e

−

t 8tend

• ◮ At t = tend

◮ Heat leaked (analytic): (T1 − T0) 1

√π Lc ≈ 0.56(T1 − T0)Lc

◮ Heat leaked (single-cell):

2Lc(T1 − T0)

• 1 − e− 1

8

• ≈ 0.24(T1 − T0)Lc

◮ For t < tend, heat leakage for single-cell case is approximately linear

in time.

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Numbers describing the system

◮ Peclet number: Pe = QinjR 4πφHD ◮ Bleed: Bl = h′ H

√ tD′

◮ Gravity number: Γ = 2πk∆ρgH2 µwQinj Where: ◮ D = λeff

aq/(ρc)eff aq

◮ D′ = λob/(ρc)ob ◮ R = φ

(ρc)co2 (ρc)eff aq

◮ h′ =

(ρc)ob (ρc)eff aq

◮ ∆ρ = ρw − ρco2

Parameter ranges:

Parameter symbol unit

• min. value
• max. value

Porosity φ 0.15 0.4 Permeability k darcy 0.013 2

• Aq. thickness

H m 10 200

• Aq. thermal conductivity

λaq W/(m K) 1.2 6.4

• Ob. thermal conductivity

λob W/(m K) 1.2 6.4

• Aq. rock density

ρaq kg/m3 2500 2800

• Ob. rock density

ρob kg/m3 2500 2800

• Aq. heat capacity

caq J/(kg K) 640 900

• Ob. heat capacity

cob J/(kg K) 640 900 Aquifer depth d m 1000 3000 Thermal gradient ∇T K/km 25 50 Injection temp. Tinj K 5 + 273.15 50 + 273.15 Injection rate ρCO2Qinj kg/s 0.1 MT 20 MT

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Ranges for Pe, Γ and Bl

Γ ∈ [3.5 × 10−3, 4.2 × 103] Pe ∈ [3.7 × 10−1, 1.4 × 104] Bl/ √ t ∈ [3.0 × 10−6, 2.5 × 10−4]

◮ These extremal values are not independent of each other, and

cannot all be reached at the same time!

◮ We eliminate parameter combinations that lead to excess pressure

buildup.

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High Peclet (1.4 × 104), High Bleed (2.3 × 10−4√ t)

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High Peclet (1.4 × 104), Low Bleed (6.0 × 10−5√ t)

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Low Peclet (3.7 × 10−1), High Bleed (1.2 × 10−5√ t)

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Low Peclet (3.7 × 10−1), Low Bleed (3.0 × 10−6√ t)

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High Bleed (2.4 × 10−4√ t), High Peclet (8.0 × 103)

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High Bleed (2.4 × 10−4√ t), Low Peclet (1.5 × 103)

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Low Bleed (3.0 × 10−6√ t), High Peclet (1.3 × 103)

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Low Bleed (3.0 × 10−6√ t), Low Peclet (2.4 × 102)

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High Γ (4.1 × 103), High Pe (2.0), High Bl (1.2 × 10−5√ t)

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High Γ (4.1 × 103), High Pe (2.0), Low Bl (3.0 × 10−6√ t)

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Result summary

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Result summary: high Γ

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Tentative conclusions

◮ Plume shape always remain unaffected by heat model (but VE is not

always able to represent it correctly)

◮ Pressure ok in most scenarios, but worse for the low Pe cases, which

also have low gravity numbers

◮ Shape is generally captured by the low-resolution overburden model,

but front position is significantly affected.

◮ The adiabatic model usually gives wildly wrong front position, but

approximately OK for low Peclet and Bleed numbers.

◮ Higher gravity numbers yield worse results for VE models ◮ A VE model able to represent thermal front shapes in the general

case would need more than two values per column.

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Acknowledgments

The work presented here was carried out with support from the Norwegian Research Council, project 243729.

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